Select The Correct Answer.What Is This Equation Rewritten In Logarithmic Form? $9^x=3$A. $\log_9 3 = X$B. $\log_x 3 = 9$C. $\log_3 9 = X$D. $\log_3 X = 9$

Introduction

Logarithmic equations are a fundamental concept in mathematics, and understanding how to rewrite them is crucial for solving various mathematical problems. In this article, we will focus on rewriting the equation $9^x=3$ in logarithmic form and explore the different options available.

What is Logarithmic Form?

Before we dive into rewriting the equation, let's briefly discuss what logarithmic form is. Logarithmic form is a way of expressing an exponential equation in a different format. It involves using logarithms to rewrite the equation in a more manageable form. The general form of a logarithmic equation is $\log_a b = c$, where $a$ is the base, $b$ is the result, and $c$ is the exponent.

Rewriting the Equation

Now that we have a basic understanding of logarithmic form, let's focus on rewriting the equation $9^x=3$. To do this, we need to use the definition of logarithms, which states that $\log_a b = c$ is equivalent to $a^c = b$. In this case, we can rewrite the equation as $\log_9 3 = x$.

Option A: $\log_9 3 = x$

The first option is $\log_9 3 = x$. This is the correct answer, as we have already established that $\log_9 3 = x$ is equivalent to $9^x=3$. This option is the most straightforward and is the correct choice.

Option B: $\log_x 3 = 9$

The second option is $\log_x 3 = 9$. This option is incorrect, as the base of the logarithm is $x$, not $9$. Additionally, the result of the logarithm is $3$, not $9$.

Option C: $\log_3 9 = x$

The third option is $\log_3 9 = x$. This option is incorrect, as the base of the logarithm is $3$, not $9$. Additionally, the result of the logarithm is $2$, not $x$.

Option D: $\log_3 x = 9$

The fourth option is $\log_3 x = 9$. This option is incorrect, as the base of the logarithm is $3$, not $x$. Additionally, the result of the logarithm is $x$, not $9$.

Conclusion

In conclusion, the correct answer is $\log_9 3 = x$. This option is the most straightforward and is the correct choice. We hope this article has provided a clear understanding of how to rewrite the equation $9^x=3$ in logarithmic form.

Common Mistakes to Avoid

When rewriting equations in logarithmic form, there are several common mistakes to avoid. These include:

• Incorrect base: Make sure to use the correct base for the logarithm. In this case, the base is $9$, not $x$ or $3$.
• Incorrect result: Make sure to use the correct result for the logarithm. In this case, the result is $3$, not $9$ or $x$.
• Incorrect exponent: Make sure to use the correct exponent for the logarithm. In this case, the exponent is $x$, not $9$ or $2$.

Tips and Tricks

When rewriting equations in logarithmic form, there are several tips and tricks to keep in mind. These include:

• Use the definition of logarithms: The definition of logarithms states that $\log_a b = c$ is equivalent to $a^c = b$. Use this definition to rewrite the equation in logarithmic form.
• Identify the base: Identify the base of the logarithm and make sure to use it correctly.
• Identify the result: Identify the result of the logarithm and make sure to use it correctly.
• Check your work: Check your work to make sure that the equation is correct.

Real-World Applications

Rewriting equations in logarithmic form has several real-world applications. These include:

• Science: Logarithmic equations are used in science to model population growth, chemical reactions, and other phenomena.
• Engineering: Logarithmic equations are used in engineering to model electrical circuits, mechanical systems, and other complex systems.
• Finance: Logarithmic equations are used in finance to model stock prices, interest rates, and other financial instruments.

Conclusion

In conclusion, rewriting equations in logarithmic form is a crucial skill for mathematicians and scientists. By understanding how to rewrite the equation $9^x=3$ in logarithmic form, we can better understand the underlying mathematics and apply it to real-world problems. We hope this article has provided a clear understanding of how to rewrite the equation in logarithmic form and has provided valuable tips and tricks for mathematicians and scientists.